Dolbeault Complex on S^4\{.} and S^6\{.} through Supersymmetric Glasses

Abstract

S^4 is not a complex manifold, but it is sufficient to remove one point to make it complex. Using supersymmetry methods, we show that the Dolbeault complex (involving the holomorphic exterior derivative and its Hermitian conjugate) can be perfectly well defined in this case. We calculate the spectrum of the Dolbeault Laplacian. It involves 3 bosonic zero modes such that the Dolbeault index on S^4\{.} is equal to 3.

References in corpus (9)

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• N = 4 mechanics of general (4, 4, 0) multiplets
• Dirac Operator on Complex Manifolds and Supersymmetric Quantum Mechanics
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Cited by in corpus (5)

• Dirac Operator on Complex Manifolds and Supersymmetric Quantum Mechanics
• Quantum theory of massless (p,0)-forms
• Supersymmetric Proof of the Hirzebruch-Riemann-Roch Theorem for Non-Kähler Manifolds
• Supercharges in the HKT Supersymmetric Sigma Models
• N=2 supersymmetric S^2 -> CP^3 -> S^4 fibration viewed as superparticle mechanics